Toni Kroos and Thomas Muller put the 2012 runner-up two goals ahead after 20 minutes, but Lukas Podolski gave the hosts hope with a 55th-minute reply.

Just when Arsenal was starting to gain a foothold in the match as they searched for the equalizer, Mario Mandzukic awkwardly looped the ball over the line with 13 minutes left to re-establish the German side’s dominance.

It leaves Arsene Wenger’s out-classed team with an almost impossible task to reach the quarterfinal stage of Europe’s elite competition. The Gunners must score at least three goals in the Allianz Arena in three weeks’ time to have any hope of qualifying for the last eight.

The pressure is now as intense as it has ever been on Wenger, who had displayed such anger in his pre-match press conference on Monday as he took exception to questions about his own future.

The Frenchman had recalled his big guns as he made seven changes from the team that was dumped out of the FA Cup by Blackburn Rovers at the weekend, with Theo Walcott spearheading the attack in place of the axed Olivier Giroud.

Arsenal came flying out of the starting blocks as it took the game to Bayern but the visitors dealt them a crushing blow after seven minutes with a slickly-constructed opening goal.

Drab defending from the hosts allowed Thomas Muller’s mis-hit cross from the right flank to be seized upon by Kroos on the edge of the penalty area. The 23-year-old smashed the cross into the ground and over Wojciech Szczesny into the goal.

Bayern added a second soon after, as Daniel van Buyten latched on to a near-post corner to flash a header straight at Szczesny, who should have done better than weakly parry the ball barely a yard in front of him. While the red-and-white shirts crammed into the six-yard box barely moved, Muller pounced to prod the ball home.

Wenger’s team was shell-shocked at going two goals down and struggled to mount an attack of note in the remainder of the opening period against one of the meanest defenses in Europe. Arsenal caught a bit of a break when on the stroke of halftime, the prolific Mario Mandzukic headed powerfully wide with the goal at his mercy.

Arsenal clawed itself back into the game in the 55th minute, as Bayern conceded a goal for the first time in 664 minutes. After winning a fortuitous corner, Jack Wilshere’s curled ball traveled into the path of Podolski, who directed it over an unmanned line with what appeared to be his shoulder.

Arsenal nearly equalizer, when substitute Olivier Giroud almost scored with his first touch after seizing open a fabulous cross from Walcott. With 13 minutes remaining, though, Bayern reestablished its two-goal advantage.

More hideous defending from the home team allowed a drilled cross from Phillip Lahm to fizz across the box. Mandzukic beat Bacary Sagna to the cross to send the ball looping cruelly over Szczesny and into the net, to put Arsenal in a dire hole heading into the return leg in Munich.